Financial returns are decisively fat-tailed. Daily moves that a normal model calls once-in-the-history-of-the-universe events happen every few years.
The practical consequence. Risk estimated from a normal assumption understates tail loss by orders of magnitude. This is not a small correction - it is the difference between a survivable and a fatal position.
Sources: volatility clustering mixes normals of different variances, and genuine jumps add more. Student's t is a common tractable alternative; extreme value theory handles the tail directly.